Question

Which choice is equivalent to the expression below when x  0?

√18X^30-√9X^3+3√X^3-√2X^3

A.2√2X
B.4√X
C.2X√2X
D.√10X^3

Answer 1

$\sqrt{18x^3}-\sqrt{9x^3}+3\sqrt{x^3}-\sqrt{2x^3}\\\\=\sqrt{9x^2\cdot2x}-\sqrt{9x^2\cdot x}+3\sqrt{x^2\cdot x}-\sqrt{x^2\cdot2x}\\\\=3x\sqrt{2x}-3x\sqrt{x}+3x\sqrt{x}-x\sqrt{2x}=2x\sqrt{x}\\\\Answer:C.$

Answer 2

$\sqrt{18x^3}-\sqrt{9x^3}+3\sqrt{x^3}-\sqrt{2x^3}=\\ 3\sqrt{2x^3}-3\sqrt{x^3}+3\sqrt{x^3}-\sqrt{2x^3}=\\ 2\sqrt{2x^3}=\\ 2x\sqrt{2x}\Rightarrow C$